where \(W\left\lbrace v\in H^1(\Omega )\ :\ \sigma (v)n|_{\Gamma _C}\in L^2(\Gamma _C)\right\rbrace \)  (notice that \(V_h \subset W\) ).
Assuming that \(u\in W\) , the first contact condition () can be written as (see [1]}, [2]}):
\(\sigma ^n(u) = \left[\sigma ^n(u)-\gamma u^n\right]_{\mathbb {R}^-} = \left[P_{1,\gamma }^n(u)\right]_{\mathbb {R}^-}.\) 
